Transcript SLIDE SHOW 3 - University of St Andrews

SLIDE SHOW 3
INDUCTION EQUATION
B
2
   (v  B)    B
t
I
II
1
where  
is magnetic diffusivity

•
B changes due to transport + diffusion
•
B moves with plasma / diffuses through it
•
I
II

L0 v0

 Rm
-- * magnetic
Reynold number *
(a) If Rm << 1
 The induction equation reduces to
B
2
  B
t

B is governed by a diffusion equation
--> field variations on a scale L0
2
L0
diffuse away on time * t d  

with speed v d  L0 /t d  L
0


*
(b) If Rm >> 1
The induction equation reduces to
B
   (v  B)
t
and Ohm's law -->
E
+ vB = 0
Magnetic field is “* frozen to the plasma *”
1. Diffusion
Start with
field B0(x)
and watch
diffuse.
Current
density
QuickTime™ and a YUV420 codec decompressor are needed to see this picture.
2. Diffusion heats the corona
X-ray bright points, coronal holes, coronal loops
Coronal loops -- many tiny diffusion locations
3. Diffusion allows magnetic connections to change -- eg
when flux emerges
QuickTime™ and a
Video decompressor
are needed to see this picture.
4.
Diffusion
converts
magnetic
energy to
heat in a
Solar
Flare
Sudden
brightening in
chromosphere
& corona near
sunspots
A Solar Flare
TRACE -- T = 1.6 MK and 30 MK)
1. B diffuses &
heats plasma
to 30 MK !
QuickTime™ and a
decompressor
are needed to see this picture.
2. Heat spreads
along arcade
of loops, which
then cool
through 1.6
MK
3. The loops rise
1. If
magnetic
field
static,
then
plasma
can flow
only
along B
Example of
Plasma
Motions
along Loops
QuickT ime™ and a Video decompressor are needed to see t his picture.
2. Photosphere
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Covered with
turbulent
convection cells:
Granulation
(1 Mm)
Supergranulation
(15 Mm)
This carries magnetic field to edges of cells
Map of Photospheric Magnetic Field
White -- towards
you;
Black -- away from
you
B is
concentrated
around edges of
supergranule
cells by flow
In closeup:
B is even
concentra
ted at
edges of
granules
3. When a
magnetic
field erupts,
the plasma
is carried
with it
e.g.
Erupting
Prominence
E.g. Coronal Mass Ejection
The
SUN
TODAY
The
photo
sphere
(SOHOMDI)
Magnetic
field
(SOHOMDI)
Movie of
magnetic
field
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Chromo
sphere
(Ha Big
Bear)
Chromo
sphere
(SOHOEIT)
Corona
at 1.3
MK
(EIT)
Corona
at 1.6
MK
(EIT)
Corona
at 2.3
MK
(EIT)